Question : A certain sum of money amounts to Rs. 2200 at 5% p.a. interest and Rs. 2320 at 8% p.a. interest in the same period. The period is:
Option 1: 3 years
Option 2: 4 years
Option 3: 5 years
Option 4: 2 years
Correct Answer: 2 years
Solution :
Total amount at 8% interest = Rs. 2320
Total amount at 5% interest = Rs. 2200
Simple interest, Simple Interest, at (8 – 5=3)% = 2320 – 220 = 120
Simple Interest at 1% = $\frac{120}{3}$ = 40
⇒ SI at 5% = 40 × 5 = 200
Sum, $P$ = Total amount – Simple interest
⇒ $P$ = 2200 – 200 = Rs. 2000
Simple Interest after $n$ years = $\frac{PnR}{100}$
⇒ 200 = $\frac{2000×n×5}{100}$
⇒ $n$ = 2
Hence, the correct answer is 2 years.
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